Impact of New Experimental Data on the C2HDM: the Strong Interdependence between LHC Higgs Data and the Electron EDM

The complex two-Higgs doublet model (C2HDM) is one of the simplest extensions of the Standard Model with a source of CP-violation in the scalar sector. It has a $\mathbb{Z}_2$ symmetry, softly broken by a complex coefficient. There are four ways to implement this symmetry in the fermion sector, leading to models known as Type-I, Type-II, Lepton-Specific and Flipped. In the latter three models, there is a priori the surprising possibility that the 125 GeV Higgs boson couples mostly as a scalar to top quarks, while it couples mostly as a pseudoscalar to bottom quarks. This ``maximal'' scenario was still possible with the data available in 2017. Since then, there have been more data on the 125 GeV Higgs boson, direct searches for CP-violation in angular correlations of $\tau$-leptons produced in Higgs boson decays, new results on the electron electric dipole moment, new constraints from LHC searches for additional Higgs bosons and new results on $b\to s \gamma$ transitions. Highlighting the crucial importance of the physics results of LHC's Run 2, we combine all these experiments and show that the ``maximal'' scenario is now excluded in all models. Still, one can have a pseudoscalar component in $h \tau\bar{\tau}$ couplings in the Lepton-Specific case as large as $87\%$ of the scalar component for all mass orderings of the neutral scalar bosons.